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Vector fields on bifurcation diagrams of quasi singularities

Fawaz Alharbi, Yanlin Li
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Computing 3D Bifurcation Diagrams [PDF]

AIP Conference Proceedings, 2008
The nature and localization of critical parameter sets called bifurcations is a central issue in nonlinear dynamical system theory. Codimension‐1 bifurcations form hypersurfaces in parameter space. Some bifurcations of higher codimension can be identified as intersections of these surfaces.
D. Stiefs, T. Gross, VENTURINO, Ezio, U. Feudel   +3 more
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Qualitative bifurcation diagrams

Expert Systems, 2013
AbstractWe explore the use of qualitative reasoning to predict the behaviour of a dynamical system given a change in one of its parameters based upon a qualitative representation of its bifurcation diagram. We present three algorithms to perform this task.
Andrzej Proskurowski, Juan J. Flores, Hector Rodriguez, Arthur M. Farley   +3 more
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Geometry of bifurcation diagrams

Journal of Soviet Mathematics, 1984
The geometry of a bifurcation diagram in the base of a versal deformation of a singularity is studied for single singularities on a manifold with boundary. In particular, vector fields and groups of diffeomorphisms are studied which are defined in a neighborhood of a bifurcation diagram as are stratification of a bifurcation diagram and decomposition ...
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Experimentally Observed Bifurcation Diagrams

2002
Extensive studies of structures and materials undergoing perfect and imperfect bifurcation have been conducted. Bifurcation of structures can be highlighted, e.g., by Ziegler, 1968, 1977 [196]; Thompson and Hunt, 1973, 1984 [174], [175]; Ben-Haim and Elishakoff, 1990 [14]; Bažant and Cedolin, 1991 [12]; and references therein.
Kazuo Murota, Kiyohiro Ikeda
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Structure in the bifurcation diagram of the Duffing oscillator

Physical Review E, 1995
We identify four levels of structure in the bifurcation diagram of the two-well periodically driven Duffing oscillator, plotted as a function of increasing control parameter T, the period of the driving term. The superstructure, or bifurcation peninsula, repeats periodically as T increases by \ensuremath{\sim}2\ensuremath{\pi}, beginning and ending ...
Robert Gilmore, J. W. L. McCallum
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Hero’s journey in bifurcation diagram

Communications in Nonlinear Science and Numerical Simulation, 2012
Abstract The hero’s journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure.
P.N. Mustaro, Luiz Henrique Alves Monteiro, Luiz Henrique Alves Monteiro   +2 more
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Bifurcation diagram for a piecewise-linear circuit [PDF]

IEEE Transactions on Circuits and Systems, 1984
The bifurcation diagram of an R-L -Diode circuit driven by a sinusoidal voltage source is computed. The model of the diode is piecewise linear. Qualitatively, the same phenomena have been obtained as for the previously published computer simulation with the conventional junction diode model.
R. Duhr, Martin Hasler, A. Azzouz
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Inferring bifurcation diagrams with transformers

Chaos: An Interdisciplinary Journal of Nonlinear Science
The construction of bifurcation diagrams is an essential component of understanding nonlinear dynamical systems. The task can be challenging when one knows the equations of the dynamical system and becomes much more difficult if only the underlying data associated with the system are available.
Lyra Zhornyak, M. Ani Hsieh, Eric Forgoston   +2 more
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On the bifurcation diagram of discrete analogues for ordinary bifurcation problems

Mathematical Methods in the Applied Sciences, 1979
AbstractOrdinary bifurcation problems of the form (1) typically have at most one nontrivial, nonnegative solution for λ > 0. The paper shows that this is in general not true for discrete analogues to (1) no matter how small the step width h > 0 is chosen.
K. Kirchgassner, E. Bohl
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